Why don't Muslims celebrate Christmas?

EDIT: My original answer follows below, but I'd like to answer the feedback my comments have received from some Christians. I think that I could have made myself clearer. Muslims and Christians will never be in 100% agreement about Jesus. Muslims accept Jesus as a prophet, not as the son of God. Some Christians will quote incidences in the Bible where Jesus refers to God as his father. What I should have specified is that Muslims believe in Jesus and his prophet status, but we do not recognize the New Testament of the Bible as a completely accurate record of what he said/did. We believe the story of his birth (hence my answer below about Christmas), we believe his basic message about how to treat your fellow man, but we do not believe in a Holy Trinity, nor a Crucifixion/Resurrection. This is why, although Muslims and Christians both believe in Jesus, they believe different and, sometimes, contradictory things about him. We have the highest respect for Jesus, considering him one of the most important prophets, and would never call him a liar. We simply don't believe that he ever said he was the son of God, even if other traditions have records stating that he did.

Okay? I know the Christians have their own opinion that differs from the Muslim one, and I respect it (the Qur'an does tell us to respect the Christians and their beliefs even if we don't agree with everything. At the end of the day, both faiths lead to heaven). Now on to my original answer . . . .

Muslims believe in a long line of prophets extending back to Adam himself. This includes most of the major Biblical figures: Noah, Abraham, Moses, Jesus... some Muslims I know claim that we cannot even know exactly how many prophets there were because there were many, but I can't provide an exact reference for that.

In fact, by including people like Adam and Noah, the Muslim list of prophets is even more inclusive than the Jewish one. Jesus is an important prophet although Muslims reject the idea that he was the son of God, as well as the concept of a Trinity. Muslims all believe that Muhammad (pbuh) was the last of the prophets, and that he is the most important because he brought Islam (Judaism and Christianity are seen as earlier versions of the same divine message from the same God, but with certain differences in interpretation that caused Him to try again through Muhammad (pbuh)).

Many Muslims celebrate Muhammad's birthday (pbuh) because he is the most important of the Muslim prophet. While celebrating the birth of Jesus is not traditional because he is not the primary prophet, Muslims do believe in most of the Christmas story EXCEPT the role of God as Father. I cannot think of any specific reasons why it would be wrong to celebrate Christmas, just that it is not traditional. In homes like the one I grew up in, with one Muslim parent and one Christian parent, it can certainly happen. The first Muslim community (620s AD) lived among Jews and fasted Yom Kippur with them; ideally Muslims are to respect Christianity, Judaism, and especially the common points that they share.